No. As such there are no authorities that govern Hinduism though the Vedas are considered the "Supreme Truth". The highest authority is considered the Vedas and interpretation of Vedas give rise to various philosophies and ideologies on Hinduism. And it is up to each individual Hindu to decide what school of thought one wishes to accept or how one wishes to interpret the Vedas.
No,Since,Hinduism isnt a Religion,its a way of living,its a way to achieve Self Attainment,even God is considered as a tool to Achieve It! 'Karma hee Dharm hai'
Each individual Guru-parampara has an authority, namely the living Guru in that tradition. Of course most Hindus don't belong to or are members of lineages like that.
In a sense of religion no it's not govern by some authorities.... But Yes the law of nature governs Hinduism as it's a Dharma based on various laws of nature...it's derived from nature,the surrounding n the true science.
Yes. Guru, Sadhu and Shastra. They r the one and same. Guru is a Sadhu as he is a devotee of the lord and he will never speak out of Shastra. But Guru has to be an Authorized Guru not like we see people exploiting others in the name of Guru. He should belong to either one of the 4 disciplic succession or "Sampradaya's" namely Brahma Sampradaya, Shri Sampradaya, Rudra Sampradaya or Kumar Sampradaya as this is the way the vedic knowledge about God is descending to us. Hare Krishna